# Uniformly Diophantine Numbers in a Fixed Real Quadratic Field

 Title: Uniformly Diophantine Numbers in a Fixed Real Quadratic Field Author: McMullen, Curtis T. Citation: McMullen, Curtis T. 2009. Uniformly Diophantine numbers in a fixed real quadratic field. Compositio Mathematica 145(4): 827-844. Full Text & Related Files: uniformly_diophantine_numbers.pdf (412.2Kb; PDF) Abstract: The field $$\mathbb{Q}(\sqrt5)$$ contains the infinite sequence of uniformly bounded continued fractions $$[\overline{1, 4, 2, 3}], [\overline{1, 1, 4, 2, 1, 3}], [\overline{1, 1, 1, 4, 2, 1, 1, 3}]$$, ..., and similar patterns can be found in $$\mathbb{Q}(\sqrt d)$$ for any $$d>0$$. This paper studies the broader structure underlying these patterns, and develops related results and conjectures for closed geodesics on arithmetic manifolds, packing constants of ideals, class numbers and heights. Published Version: doi:10.1112/S0010437X09004102 Other Sources: http://www.osti.gov/eprints/topicpages/documents/record/884/2613233.html Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:9925390 Downloads of this work: